Identifier
-
Mp00122:
Dyck paths
—Elizalde-Deutsch bijection⟶
Dyck paths
Mp00032: Dyck paths —inverse zeta map⟶ Dyck paths
St000386: Dyck paths ⟶ ℤ
Values
[1,0] => [1,0] => [1,0] => 0
[1,0,1,0] => [1,1,0,0] => [1,0,1,0] => 0
[1,1,0,0] => [1,0,1,0] => [1,1,0,0] => 0
[1,0,1,0,1,0] => [1,1,0,0,1,0] => [1,1,0,1,0,0] => 0
[1,0,1,1,0,0] => [1,1,0,1,0,0] => [1,1,0,0,1,0] => 1
[1,1,0,0,1,0] => [1,1,1,0,0,0] => [1,0,1,0,1,0] => 0
[1,1,0,1,0,0] => [1,0,1,1,0,0] => [1,0,1,1,0,0] => 0
[1,1,1,0,0,0] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0] => 0
[1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0] => 0
[1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 1
[1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 0
[1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0] => 1
[1,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0] => 0
[1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 2
[1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0] => 0
[1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 1
[1,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0] => 0
[1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,0,0] => 0
[1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 1
[1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0] => 0
[1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 0
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => 2
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 0
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 2
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => 0
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 1
>>> Load all 1417 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 0
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 2
[1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 2
[1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => 0
[1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => 1
[1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 2
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 0
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => 1
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 0
[1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 3
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 0
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 0
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 2
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 0
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 0
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 2
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 0
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 0
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 2
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 3
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 0
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 0
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 2
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 2
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 3
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 2
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 2
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 0
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 3
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 3
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 2
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 0
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 0
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => 3
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 3
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 2
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 2
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 2
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => 2
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 0
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 0
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 2
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 1
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 1
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 0
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 3
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 3
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 0
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 2
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 2
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 0
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 1
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 3
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 3
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 2
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 2
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 2
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 3
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 2
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 2
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => 1
[] => [] => [] => 0
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => 1
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => 4
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => 3
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => 3
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0] => 3
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => 2
[1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => 1
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
4,1 8,6 16,24,2 32,80,20 64,240,120,5
$F_{1} = 1$
$F_{2} = 2$
$F_{3} = 4 + q$
$F_{4} = 8 + 6\ q$
$F_{5} = 16 + 24\ q + 2\ q^{2}$
$F_{6} = 32 + 80\ q + 20\ q^{2}$
$F_{7} = 64 + 240\ q + 120\ q^{2} + 5\ q^{3}$
Description
The number of factors DDU in a Dyck path.
Map
inverse zeta map
Description
The inverse zeta map on Dyck paths.
See its inverse, the zeta map Mp00030zeta map, for the definition and details.
See its inverse, the zeta map Mp00030zeta map, for the definition and details.
Map
Elizalde-Deutsch bijection
Description
The Elizalde-Deutsch bijection on Dyck paths.
.Let $n$ be the length of the Dyck path. Consider the steps $1,n,2,n-1,\dots$ of $D$. When considering the $i$-th step its corresponding matching step has not yet been read, let the $i$-th step of the image of $D$ be an up step, otherwise let it be a down step.
.Let $n$ be the length of the Dyck path. Consider the steps $1,n,2,n-1,\dots$ of $D$. When considering the $i$-th step its corresponding matching step has not yet been read, let the $i$-th step of the image of $D$ be an up step, otherwise let it be a down step.
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